Saturday, October 25th, 2014

    This week, we covered more proofs, however this week was the "end" of proofs for the rest of the section. I honestly do see us using proofs later regardless of us being "finished" covering them. We ended up covering disproving and allowed inferences in more detail through the middle of the week. I found all the inferences extremely helpful to me, they will end up being used by not only me, but most students in the class as an exemplary study aid. A lot of the inferences given, although common sense, will still help many students, including me, when writing proofs on tests, speeding up our thinking processes. As for disproving, I found it quite easy to grasp: simply take the proof, and negate it, then prove that to disprove. I feel I may be wrong, as looking back at my notes, the statement doesn't look like a full negation; the example we took in class being what I'm referring to (For all x in a set of X, for all y in a set of Y, P(x,y) implies Q(x,y)). I'll need to look into this more in depth come next week of class, I'll end up talking to Prof. Heap about it. The rest of the week consisted of looking at sorting algorithms that I had recently learned about in CSC108 the previous year. Insertion sort and Selection sort were two of the algorithms that were referenced in class, I'd always had difficulty determining between the two, but, this year I feel I have a better grasp on them. As for Friday, we did a sorting exercise, which I found interesting, cutting the number of pennies in half from drawer to drawer to obtain a certain number. It was insightful as an exercise, but I feel I wouldn't be able to do something like that in a test environment. For this week, I felt more comfortable with the material, and I will continue to use the strategies I have listed in previous posts to keep comfortable.  

Sunday October 19th, 2014

    To start off, obviously today's date isn't the 19th, but this is an update on the previous week. I had put off writing this post for a bit since I didn't feel I had learned anything different or felt that I personally didn't understand any more than I did the week before Thanksgiving week. To recap this past week, we continued running through proofs and learned a different way to structure them, which I found quite useful to trim away a good amount of time while writing proofs, which will come in handy come test/exam days. Using the tinier starting bits of proof to conclude will really help me in these situations. Also, throughout the week, we looked at several different ways to write proofs, one being by case. This one stood out to me, simply because I found the step unnecessary to prove for separate cases, but I digress. I mean, this type of proof will be useful, but to me at the moment, it seems like a bit of unnecessary work. I am still having difficulties with proofs, but I know I'll be able to understand them with time and practice.
    Such as today in tutorial, I had a breakthrough (or at least I hope I did) in writing a full proof. The question, although simple, was still conceptually difficult to me, so I tried my hardest to understand it, following the necessary steps: proving the "for all" quantifiers with a statement that all variables under this quantifier are generic in the set they are meant to belong to, setting up the necessary bookends, but then it came to choosing a number to represent a variable, and I froze for a while. I looked at the question more carefully and I read it out in plain english and the lightbulb went off almost immediately for what I had needed to do. I felt pretty good about it, but I'm still not 100% confident that I got the answer right, even though I feel my proof still holds well. As for now, I'll continue practicing and taking whatever results I get as a learning experience.

Saturday, October 11th, 2014

Good Afternoon,

    This week was surprisingly clearer than last week was when it came to proofs, although I am still extremely cloudy on how to properly structure and define them. Last week I was almost completely lost in the topic of proofs, both structure and definition. I didn't entirely understand the concepts related to existential and universal statements, but after this week, I realize that for a universal statement, you need to assume that that number n is a generic number of whichever set the universal statement points to. As well as for existential statements, I learned clearly that when referring to variable n as something that exists in some set, we need to prove that n exists, so we name n as some number/variable. That is what I took from lectures and tutorial, but I am not concrete on it.
    Speaking on the tutorial this week, I feel my quiz went better than in previous weeks simply because I spoke up and paid a little closer attention to the TA's examples and explanation. My quiz was breezier for me to run through than the previous 2, as the first two quizzes I felt I didn't take the necessary steps to really further my learning in checking over the examples and really reading into the material. Noting this, I'll make this a standard practice for the future to come in this course. There's nothing really more I can go into detail about as I have yet to fully comprehend proofs enough to write about them at length, so for now, I'll be ending this SLOG post until next week.

Damon Kissoon

Saturday, October 4th, 2014

Good Afternoon,

    I know this post is later than it should have been and I'm one week short of updates, but I had a sickness last week. I was diagnosed with (insert disease that I'd rather not share with the public here) which caused me to not be able to attend school or even easily get up out of bed for the week of September 21st. Since then, I've gotten a lot better, handed Prof. Heap a doctor's note, (nameless disease) is slowly working its virus out of my system thanks to modern medicine and good bed rest, and I was able to go to school this past week, albeit a little left out on certain techniques like DeMorgan's Law and other things I may have missed last week. That being left out, I can discuss things I may have missed, as well as things I have understood over this week.
    Let me start by talking about some things I may have left out in the previous SLOG, such as conjunction, disjunction and negation. These three topics I have encountered in previous courses such as CSC108, where, in Python, I had tweaked around with aspects such as programming using boolean operators. These aspects, through logic however, were also tweaked slightly. The "And" operator still held the same precedence: in Python, one statement is not True without the other statement also being True; logically this turns out to be the same in CSC165. However, "Or" operated slightly differently, where through Python, the entire statement would be true if either statement was true. In logic, or operates as an "and/or" type of inclusive statement, that involves both the antecedent and the consequent in making a statement true, though not really combining them. It's a very different concept to grasp, and I'm not entirely sure if I have the right handle on it, but this is what I pick up from disjunction. Negation was much easier on me however, switching out conjunction for disjunction, existential for universal, and P implying Q for P implying not Q. I found negation relatively easy simply because all you truly need to know is that the symbols flip, exists becomes for all, and the only way to negate an implication is by creating the statement as P and not Q.
    As for this past week, regardless on missing out on several things last week, I did pick up on some key concepts. During talking about constructing proofs, I learned about how we'd be able to switch around similar statements, as long as each statement involved the same universal or existential quantifier. For example: "For all m in a set of natural numbers, and for all n in a set of natural numbers, the product of m and n is a natural number." M and n's positions can be changed around so long as the quantifiers match up. The same goes for existential quantifiers, meaning the two statements can be flipped if the meaning changed to there exists for both statements.
    For concepts I still remain fuzzy on, I'm not entirely sure of how to fully construct proofs, but I'm hoping that Prof. Heap will go into more detail about these next week. What I do understand is how a proof is meant to be structured: statements that all imply something about the one before that fully prove the first implication. I am still unclear on how these statements are originally formed, but I think through the first implication, I would be able to get a proof going. Otherwise, it remains unclear. So, for this SLOG, I have parted with all of my ideas, and I hope they will somehow help me as a reflection on my previous knowledge, and hopefully help me to end up to learn further.